MATA30H3 Lecture Notes - Lecture 5: Trigonometric Functions, Inverse Trigonometric Functions
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Must define this to be range range of sinq is [-1, 1] So (cid:449)e ca(cid:374) restrict the do(cid:373)ai(cid:374) to (cid:373)ake o(cid:374)e to one. One to one 0 { (cid:4666)(cid:882)(cid:4667) = (cid:882) Restrict domain a = [ (cid:2870) , (cid:2870): so : [ (cid:2870) , (cid:2870)] [-1, 1] 1: [-1, 1] [ (cid:2870) , (cid:2870): therefore, output is always between [ (cid:2870) , (cid:2870)] 2: x = cos ((cid:2870)(cid:2871) ) = -(cid:2869)(cid:2870, y = sin ((cid:2870)(cid:2871) ) = (cid:2871)(cid:2870, z = tan ((cid:2870)(cid:2871) ) = - (cid:885) Arctanz = arctan (tan(cid:2870)(cid:2871) (cid:895) (cid:2870)(cid:2871) (i). Arcsiny = arcsin (sin (cid:2870)(cid:2871) (cid:895) (cid:2870)(cid:2871) (cid:2870)(cid:2871)(cid:1488)[(cid:882),] *(cid:2870)(cid:2871) is not a possible output for fxn (cid:2870)(cid:2871) (cid:1489)(cid:4666) (cid:2870),(cid:2870)(cid:4667) If x (cid:1488)[ (cid:883),(cid:883)] like x = correct * y = (cid:2871)(cid:2870) , y (cid:1488)[ (cid:883),(cid:883)] Arctanz exists for all : tan x = z can be a value between all . So if x (cid:1489)[ (cid:883),(cid:883)] arccosx & arcsinx.